Dynamic analysis of a helical gear pair under uncertain bearings properties

Resumo

The complexity of the dynamic response of gear pairs models may vary, depending on the approximation
chosen to time-varying mesh stiffness. When uncertainties are considered in the model, another layer of difficulty
is added and the computational cost increases. To solve the stochastic model, Monte Carlo methods are usually
implemented. However, the large number of samples plus the complex deterministic model may make the problem
unfeasible to solve. The use of stochastic collocation with generalized polynomial chaos expansion can diminish
the number of samples, allowing the study of complex gear pairs. In this work, the stochastic dynamical response
of a pair of helical gears is analyzed. The mesh stiffness is calculated by the accumulated potential energy method
and uncertainties on the translational bearing’s stiffness are considered. The stochastic dynamical response of the
system was approximated through a generalized polynomial chaos expansion and the expansion coefficients were
evaluated by the stochastic collocation.